Multiple Cohen strongly summing operators, ideals, coherence and compatibility

TL;DR

This paper introduces and analyzes classes of multiple Cohen strongly p-summing multilinear operators and polynomials, exploring their properties within the framework of multilinear and polynomial ideals and holomorphy types.

Contribution

It extends the theory of multiple summing multilinear operators by defining Cohen strongly p-summing classes and examining their ideal and holomorphic properties.

Findings

Established the classes of multiple Cohen strongly p-summing operators and polynomials.

Proved their compatibility with multilinear and polynomial ideal frameworks.

Applied the Pietsch Domination Theorem in this context.

Abstract

Considering the successful theory of multiple summing multilinear operators as a prototype, we introduce the classes of multiple Cohen strongly p-summing multilinear operators and polynomials. The adequacy of these classes under the viewpoint of the theory of multilinear and polynomial ideals and holomorphy types is discussed in detail. Some abstract results are also proved in the abstract setting of the full general Pietsch Domination Theorem due to Pellegrino, Santos and Seoane-Sep\'{u}lveda.